Agent-Based Modeling and Simulation of
Mosquito-Borne Disease Transmission
Akshay Jindal
Shrisha Rao
International Institute of Information Technology,
Bangalore
International Institute of Information Technology,
Bangalore
[email protected]
[email protected]
ABSTRACT
Mosquito-borne diseases, such as chikungunya, dengue, and
malaria, are re-emerging and expanding to new and formerly
unaffected places, leading to a need for models which can
track their evolution and thus help with public policy and
epidemiological studies. Such diseases’ evolution is driven
by the interactions between hosts and vectors, and is thus
heavily dependent on factors like host and vector population
distributions and mobility, and geographical and weather
conditions. Traditionally used mathematical models fail to
capture such issues, thereby creating a gap between what
epidemiologists and disease modelers can provide, and what
public health policy requires. We give a generalized agentbased model (ABM) which overcomes these limitations by
careful integration of geographic information (GIS) and census data to account for the spatial movement of infections,
and climate data to capture the temporal nature of an epidemc. It captures the disorganized interactions of hosts and
vectors at a micro-scale by explicitly modeling each human
and mosquito to simulate the complex trajectories of disease outbreaks (even those have yet to occur), and makes it
possible to test the efficacy of various public health policies.
This model also suggests that it is possible to estimate hardto-determine parameters about vectors (e.g., a mosquito’s
sensing distance), through simple model calibration. Unlike
previous solutions, our model is trained and validated using real data from a 2013-14 chikungunya epidemic in the
Caribbean and is seen to give accurate results.
Keywords
Chikungunya; Computational Epidemiology; Mosquitoes; Public Health; Simulation
1.
INTRODUCTION
Vector-borne diseases, of which mosquito-borne diseases
are the largest subset, account for more than 17% of all
infectious diseases, and cause more than 1 million deaths
every year [49]. Adding to their high fatality rates, they
also have high attack rates, and are very prone to mutation, leading to recurrent infections and a lack of single vaccine [50]. This creates the need for more proactive soluAppears in: Proc. of the 16th International Conference on
Autonomous Agents and Multiagent Systems (AAMAS 2017),
S. Das, E. Durfee, K. Larson, M. Winikoff (eds.),
May 8–12, 2017, São Paulo, Brazil.
Copyright © 2017, International Foundation for Autonomous Agents
and Multiagent Systems (www.ifaamas.org). All rights reserved.
426
tions for their containment—particularly, solutions capable
of tracking the trajectory of the infection evolution at a very
fine granularity. However, modeling the complicated relationships among human-mosquito-pathogen continues to be
a challenging problem faced by all epidemiologists and public health experts.
Traditionally adopted mathematical approaches for this
purpose are the differential equation models [21] and meanfield type models [30], which fail to track spatial and temporal factors like population density and dynamics, and ignore
the spatial implications within the system, thereby creating a huge gap between what epidemiologists can deliver
and and what public health policy makers would like [15,
41]. This neglect of spatial and temporal components in
epidemic model formulation can be resolved by the use of
the agent-based modeling paradigm [44]
We give an agent-based model which overcomes the above
limitations of prior mathematical models, to adequately capture the spread of vector-borne diseases at a fine granularity, and show how it can contribute to low-level policy
design such as testing intervention strategies in epidemic
life-cycle. It captures the complex relationship between humans, mosquitoes, and pathogens by modeling them individually at a micro scale using simple adaptive rules, and
letting them interact. The environment is structured using
multi-layered GIS data to address the space implications in
disease proliferation, is realistically initialized using census
data to account for variable population density, and driven
by climate (precipitation + temperature) data to correctly
capture disease vector dynamics. Each of these three agent
populations have been designed to imitate the characteristic
behavior of the vector-borne diseases:
1. Our human agent population approximates the mobility patterns across various population sub-groups
while being sensitive to the spreading infection to adequately capture the spatial movement of the infection.
This overcomes the usual drawback of the aggregated
nature of mathematical models and helps us analyze
various intervention strategies.
2. To account for the seasonal nature of an epidemic,
the mosquito agent population is made to be heavily dependent on precipitation data and availability
of resources as these are known to be major factors
in disease propagation [17, 4]. This captures the inherently disordered nature of such epidemics. One
of our novel contributions here is the incorporation
of the climate sensitive complex reproduction cycle of
mosquitoes within the mosquito agent. Every stage of
a mosquito is separately modeled with its age being
a linear function of temperature and time to closely
resemble the mosquito population in nature.
to study disease propagation, disregarding other dominant
factors which severely undermines the prediction accuracy
of such models. Also, none of these models are validated using real data making their results wildly unpredictable and
impossible to compare with other models.
In summary, our novel contributions are:
3. Our infection model is designed as a state machine
with variable transition probabilities, making it easily generalizable to a large subset of mosquito-borne
diseases.
(i) A framework for incorporating climate sensitive complex reproduction cycle of mosquitoes in the mosquito
agent.
The epidemic emerging from our model is calibrated and
validated using data from the 2013-14 chikungunya epidemic
on some Caribbean islands, as a proof of concept. The model
predictions are 93.3% accurate on the test data of the reported cases, with the small gap suggesting that there were
some cases which went unreported, which matches with reality, where a lot of chikungunya cases go unreported due to
the non-fatal nature of the disease. We also show how our
model can be utilized to estimate some vector parameters
like mosquito sensory range, mortality rate, etc. which are
hard to determine directly. Furthermore, we test two prevention strategies, LSM and ITN+IRS, and the results show
that for a small urban tropical area, LSM is more effective in
terms of cost, mosquito control, and infection elimination.
Also, considering that in most cases a mosquito’s life cycle
is not greatly dependent on the presence or absence of the
infection due to their short lifespan [19], our model can be
easily adapted for other mosquito-borne diseases with minor
modifications. To adopt the model for some other mosquitoborne disease, we only need to modify the values of relevant
parameters based on the new vector’s and pathogen’s behavior, and calibrate others using data from past epidemic
of the same disease.
There are some ABMs proposed to model the spread of
vector-borne diseases. Dommar et al. [17] developed an
ABM to model chikungunya outbreaks, and indicate that
topology and precipitation are dominant factors in vectorborne disease propagation. Teng et al. [16] also provide a
similar model for simulating dengue spread. However, neither of these accounts for human mobility patterns, thereby
neglecting the major source of spatial movement of infections. Arifin et al. [33] provide a framework for effectively using multi-layered GIS data in an ABM-based malaria study.
Illangakoon et al. [27] explore the efficacy of ABMs for studying malaria prevalence and transmission, and show how human mobility patterns have a strong affect on disease transmission. Ying et al. [4] study the effect of spatial heterogeneity on mosquito populations. All of these only focus on the
spatial nature of the epidemic and are inconsiderate of the
climatic conditions, a leading contributor to vector dynamics. Mniszewski et al. [34] leverage the efficacy of differential
models by proposing a “hybrid network patch model” to give
insights into the effect of variable probabilities in infection
model on the ABM; and Isidoro et al. [28] show the utility
of ABMs to try out different mosquito control strategies.
However, both of these operate on random topologies and
thus do not correctly capture the host-vector interactions.
Miksch et al. [32] show the potential of ABMs to recreate
real life epidemics through model parameterization and calibration but in a manner very limited to a particular disease
and location. Our work is a significant improvement over
them as most of these models operate at a large scale with
granularity ranging from human crowd to cities network [16,
17, 33, 34], making them infeasible for low level policy design. They also focus on a very narrow set of parameters
(ii) A generalized mechanism for an epidemic ABM’s calibration and validation.
(iii) A method for estimating hard-to-determine vector parameters like mosquito sensory range, using ABMs.
(iv) Methods for testing different policies like intervention
strategies using our model. (We also have a comparative analysis of existing ABMs for modeling vectorborne diseases and our model.)
In Section 2, we give a detailed explanation of our model
design and its intrinsic workings. Here, we also describe our
simulation approach and the data-set used for validation.
In Section 3, we explain our model parameterization and
calibration, and discuss our model’s performance on the past
epidemic data. In Section 4, we show how our model can
be used for policy formulation by comparing two popular
mosquito prevention techniques. Finally, we conclude with
the current state of our model and some thoughts for future
directions in Section 5.
2. MODELING DISEASE TRANSMISSION
The modeling of the effects of climate and topology on
vector behavior, and the patterns of human mobility, is a
desideratum in the epidemiology of vector-borne diseases.
Here, we present our agent-based model which successfully
captures these effects in a disease’s evolution at an adequate
scale. The simulation strategy we adopted to qualitatively
analyze our model is also explained here.
2.1 Agent-Based Model
The agent-based model presented here represents the cumulative effects of the behaviors of individual humans and
mosquitoes in an urban environment while noting the biological trajectory of the spreading infection. It is composed
of three parts: The first is a small modification of the popular SEIR model [43] to describe the infection life cycle. The
second describes the vector distribution, interaction capabilities with the immediate environment and their dependency
on the climatic conditions. The third presents the laws governing the daily behavior/movements of human agents, and
is used to stratify the human population. The scale considered is at city level, and agent granularity is at the level of an
individual human and an individual mosquito. The following sections describe the three agents and the environment
they interact in.
2.1.1 Infection Model
Mosquito-borne diseases are transmitted human-to-mosquito
and mosquito-to-human. Symptoms vary but are generally
classifiable into two stages: intrinsic incubation period, and
infectious state. Incubation is when a mosquito has successfully infected a human and the pathogen has started
multiplying inside the host body. Depending on the disease,
427
a person may or may not be contagious during this stage.
The infectious state is when the pathogen has multiplied
and reached a certain threshold, and the human has possibly started to show symptoms. The probability of pathogen
transmission is very high during this period. Considering
that a lot of vector-borne diseases are known to have significant incubation periods (malaria, dengue, chikungunya,
etc.), the SEIR model (Susceptible → Exposed → Infectious
→ Recovered) was chosen as its exposed state addresses the
incubation period. The susceptible state is when an individual is vulnerable to infection by the pathogen. An individual
is said to be exposed when he is carrying infection but is not
yet contagious. The infected state is when the individual has
started showing symptoms and is ready to infect a mosquito.
Once the infection has passed, the individual enters the recovered state. Whether a recovered person gains a lifetime
immunity is determined by the disease. Figure 1 shows the
transition of an individual between the four states and their
respective transition probabilities and average time spent
in each state. The arrows in Figure 1 represents transition
probabilities between connected states. Chronic recovered is
the state when the person has recovered from the infection
and is no longer contagious, but still has symptoms of the
disease. It is given as an extension to the recovered state because a lot of mosquito-borne diseases are known to exhibit
such behavior [34].
Infection in mosquitoes follows a similar cycle, except they
do not recover once they have been infected. When a susceptible female mosquito bites an infected human, it gets infected with a non-zero probability. If the mosquito acquires
the pathogen, it multiplies in the mosquito till it reaches
enough strength to infect some other susceptible human,
thereby completing a cycle. This period is called the extrinsic incubation period.
and sensory range (Sr ). Flying speed and maximum distance bound the spatial movements of a mosquito agent.
Target locations are assigned to a mosquito within a circle of radius Fr at the start of the active period, and the
mosquito moves from one location to another with speed Fs .
The active period As to Ae are the hours between which the
mosquito is actively searching for a blood meal or ovipositioning sites. Maximum number of meals Mm bounds the
number of bites a mosquito is going to take in a day. Mortality rate Mr is the probability of a mosquito dying on a
given day due to some natural circumstance. Ovipositioning
characteristics include Pm : probability of an adult female to
mate successfully; and Oc → [0,1]: whether the mosquito
lays egg on a single ovipositioning site or spreads them over
multiple such sites. Sex ratio (Pf ) is the probability that the
hatching egg will be female. The sex ratio is relevant as only
female mosquitoes bite humans and lay eggs; males have no
direct role in the spread of infectious diseases. Sensory range
determines how far a mosquito is aware of its surroundings.
If a human agent or a water source comes within a radius of
Sr of mosquito agent, only then may a mosquito target it.
All these parameters were determined to be essential to
disease propagation (as they directly affect the mosquito
population and their behavior relative to the environment)
and may vary across mosquito species. For example, female
Anopheles mosquitoes are generally active during night, while
Aedes mosquitoes are day-biting. Similarly, Aedes albopictus have more meals as compared to Aedes Aegypti because
of their rapid bites, which generally keep their blood meals
short [7, 29].
Figure 2 shows a flow chart of how all the above parameters are connected together. A mosquito agent is created in
one of the water sources in the environment. There appears
to have been no research with definitive results to mathematically model mosquito movements. Some evidence suggests
that simple random walk simulations give remarkably good
approximation of real data acquired through mark-releaserecapture field trials [45]. Thus, this study models mosquito
movements as random walks in a radius of Fr /day with a
survival rate of (1-Mr )/day. If it is the active period of
a mosquito, it starts moving randomly till a human agent
comes within its sensory range. Then it follows a targeted
approach and feeds on the human. This is the only stage
when the infection propagates between existing agents. If a
mosquito bites an infected human then it gets itself infected
with a probability β, and when such an infected mosquito
bites a susceptible human, it infects the human with probability α. If the mosquito has reached its Mm limit, it
rests. Every day, with probability Pm , a mosquito’s state is
changed to carrying eggs. If the mosquito is carrying eggs,
it continues to feed on human agents till its eggs are mature
enough to be laid. A mosquito needs at least one meal after
mating for the eggs to mature [7]. The maturation period τ
is determined as a function of the temperature θ in °Celsius
(equation (1)).
Figure 1: Infection Model: Infection progression states in
humans
τ = 3 + |θ − 21|/5
2.1.2 Mosquito Agents
(1)
Three days is the time taken to mature eggs at the ideal
temperature of 21°C [13, 10]. The maturation period was
approximated to be decreasing linearly with respect to the
difference of temperature from ideal temperature, and the
slope was derived from the graph of Ae. aegypti (the primary vector in validation case study) at different tempera-
The mosquito agents move through the geographical space
and are characterized by the following parameters: flying
speed (Fs ), maximum distance (Fr ), active period (As ,Ae ),
maximum number of meals in a day (Mm ), mortality rate
(Mr ), ovipositioning characteristics (Pm ,Oc ), sex ratio (Pf ),
428
tures [10, 46, 20]. Once a mosquito mates successfully, the
time required for the batch of eggs to mature is set to τ as
calculated by that day’s temperature.
Once the eggs have matured, the mosquito starts looking
for ovipositioning sites (water sources) and lays 100 eggs at
once or over time at different sites determined by Oc . For
simplicity, all the three aquatic stages of mosquito life cycle
(egg, larva and pupa) have been modeled as eggs, and will
be referred as such throughout this article. The time taken
by eggs to turn into an adult mosquito µ, is also a function
of temperature θ, but eggs may die before hatching if their
water source dries up and is not refilled [13]. The function
(equation (2)) was approximated using the average life cycle
of Ae. aegypti (aquatic phases) [7] and effects of temperature
on them [35].
µ = µegg + µlarve + µpupae
= (2 + |(θ − 25)|/2) + (2) + (4 + |(θ − 25)|/2|)
(2)
= 8 + |(θ − 25)|
Once a batch of egg is laid, the time each egg will spend
in aquatic state before evolving into adult mosquito is set to
µ, calculated according to that day’s temperature.
Due to lack of enough published empirical evidence, both
the above equations ( (1) and (2)) were derived with the
assumption that there is no drastic change of temperature
(< ±5o C) between consecutive days. Eggs turn into adult
female mosquitoes with a probability Pf ; male mosquitoes
are discarded by the model as they do not directly contribute
to disease propagation.
2.1.3 Human Agents
The ABM tries to realistically represent the average daily
behavior of an individual in an urban landscape. Considering that mosquitoes move in a relatively short range, the
long-distance spatial movement of infection through the city
happens mostly as a result of displacement of human agents.
Thus, human agents were divided into four general categories based on their mobility patterns, based on where
they gather in groups and how often they go near potential
mosquito breeding grounds like lakes (as shown in Figure 3):
• Type 1: These human agents leave their assigned buildings at 7:00 a.m. for school and may take up to 30 minutes to reach the school. They stay there till 3:00 p.m.
and come back to their respective dwellings. From
there, with probability Pp1 an agent goes to a park at
4:00 p.m. and comes back at 7:00 p.m., after which it
stays in place till next morning. Overall commuting
takes at most 2 hours.
Figure 2: Mosquito Agents: Movement, feeding and reproduction behaviors of a mosquito
category is determined from the age distribution in the census data. The agents commute using the road network using
the shortest path to their target location. Each agent has
an attribute called state which depicts which stage (SEIR)
it is in. Once a susceptible agent is bitten by an infected
mosquito, it enters the exposed state with probability β.
An exposed agent carries on its daily activity and is mainly
responsible for the spatial movement of infection through
the city. Once the agent has entered the infectious state, it
stays in its home till it has recovered. It may stay in recovered (immune) state or move to susceptible state depending
on the disease.
• Type 2: Similar to Type 1, but the initial destination
is office and the probability of going to a park is Pp2 ,
which is less than Pp1 .
• Type 3: These are agents that are continuously on the
move. They leave their assigned buildings at 7:00 a.m.
and move in between buildings every two hours. They
come back to their dwellings at 7:00 p.m. and stay
there till next morning.
2.1.4 Environment
• Type 4: These are stationary agents who do not involve themselves in any dynamic activity; they stay in
their specific buildings throughout the day.
In this model, an infected mosquito is considered to lay
infected eggs, as has been observed in the case of dengue
and chikungunya [8]. Such infected eggs develop into infected adult mosquitoes. Figure 4 gives a flow diagram to
describe the infection propagation among vector and human
During initialization of the model, each agent is assigned
a category and a building. The number of agents in each
429
The model uses two-layered geo-referenced GIS data of a
city to realistically represent spatial movements of an individual in an urban setting. The first layer consists of buildings which include homes, offices and schools, parks and stationary water sources like lakes which are an integral part of
a vector’s life cycle. The second layer depicts the road network connecting these buildings, and all human agents move
on this network. To simplify the model, the distribution of
human agents in first layer is initialized randomly. A small
subset of buildings are assigned as schools and offices, and
one park with lake/pond is introduced. The model combines these GIS data with the weather information of the
location which is integral in the study of vector agents. It
consists of daily temperature and precipitation data. Using these parameters, the development cycles of mosquitoes
and pathogens are determined. Small water patches, which
may serve as mosquito breeding grounds, are introduced after every rainfall and their number depends on the extent
of rainfall. (Small puddles cease to exist in less than a week
if it does not rain in between, while large water bodies can
persist for months or more.)
For the purpose of this study, GIS data of Luneray, a
commune in Haute-Normandie region in northern France,
was used to model a general urban setting, and was initialized with human population of 1000, mosquito population
of 2000, and 500 mosquito eggs. This relatively low ratio
of mosquito/human was necessary to keep the model computationally tractable, but was accounted for by tuning the
mosquito mortality rate. It was then adapted and scaled to
the case studies using the corresponding location’s census
data, population density, and climate information. A park
with a lake was separately added as it was not a part of the
available GIS data. For the purpose of subjective analysis of
the model, an animated visualization of the simulation was
generated using GAMA platform.
Figure 3: Human Agents: Daily activities of human
agents
agents. An infection is transferred to a human from an infected mosquito with probability α, and infected human to
mosquito with probability β.
2.2 Simulation
As a proof of concept, an application of the model was
used for simulation of a case study of a past epidemic of
a mosquito-borne disease. The model was used to predict
the trajectory of the epidemic and the results were checked
against real data. Two intervention strategies were also
tested and analyzed. For the purpose of the demonstration, some model parameters needed to be tuned to fit that
particular scenario. We used a training data set containing
the data from a previous epidemic of the same disease in a
similar location to the testing site. Once all parameters are
determined which provided reasonably accurate results on
training data, the simulation is ran for the testing site.
(a) Mosquito Feeding
2.2.1 Case Study
(b) Mosquito
Ovipositioning
For this study, simulation of outbreak of chikungunya in
the Caribbean region is used to illustrate the given framework. For training the model, data from the 2013-14 chikungunya epidemic in Saint Martin was used. Saint Martin,
with a population of fewer than 75,000, was the epicenter of
the Caribbean epidemic. In December 2013, two laboratoryconfirmed non-imported cases were reported for the first
time in the Caribbean in the district of Ocean Pond, close
to the border of the Dutch side Sint Maarten. The model
trained on this data was tested on epidemic data from another Caribbean island, St. Barthélemy. As with the rest
of the Caribbean, residents of St Barthélemy had never en-
(c) Egg Hatching
Figure 4: Disease Transmission Cycle: Possible scenarios of disease transmission
430
countered the virus before, and had no existing immunity.
The female Ae. aegypti mosquito was taken as the vector
in the simulation, as it was the primary vector of the 2014
CHIKV outbreak in the Caribbean [36].
the area is likewise smaller, the model was initialized with
500 human individuals and 500 mosquitoes during testing.
This relatively low ratio of mosquito/human was accounted
for by significantly reducing the mosquito mortality rate to
0.05/day (in comparison to the typically accepted rate of
0.2/day).
Uni-variate sensitivity analysis was conducted, i.e., model
outcomes were analyzed with respect to one parameter at a
time. The first parameter was a mosquito’s sensory range
Sr , which was tested for six different values and error in
fitting was recorded for each value as shown in Figure 5.
2.2.2 Data
Chikungunya epidemic data were taken via the sentinel
network in Guadeloupe, Martinique, Saint Barthélemy and
Saint Martin [47]. It was compiled together and made publicly available on a weekly basis by PAHO WHO [39]. Most
epidemics only last for a few months. Also, only 3 months
of data on confirmed cases was made publicly available by
PAHO WHO. Therefore, we simulated a duration of 3 months
starting from January, 2013 for validation purpose. Weather
information was taken from [38] and interpolated to get daily
temperature and rainfall data. Lunerays’s GIS data were
made openly available by GAMA [2]. Census information
was taken from [6].
2.2.3 Simulation Toolkit
For the simulation of the ABM, GAMA was chosen as the
platform due to its data-driven ability and intuitive agentbased language [42, 23].
3.
MODEL VALIDATION AND RESULTS
Figure 5: MSE: Mean-Squared Error recorded for different
Sr values (Mm = 2)
3.1 Parameterization and Initialization
Summarizing the above model, the following are parameters that drive the model: Mosquito Parameters (Fs , Fr ,
As , Ae , Mm , Mr , Pm , Oc , Pf , Sr ), Human Parameters
(Pp1 ,Pp2 ), Infection Cycle Parameters (Ne , Ni , Prc , Pirc )
and Infection Transmission Cycle Parameters (α, β). Of
these parameters, Sr , Mm , Pf , Pm , α and β were tuned
during the training of the model due to the lack of any concrete empirical evidence of their values, while the value of
others were compiled together from various sources. Some
detailed description of the parameters and their sources is
provided as Table 1. The number of schools, offices and
households were initialized using census data [6]. Buildings
with the largest areas in the GIS data were assigned to be
schools and offices randomly.
The error metric used was mean-squared error Equation
3 (where, n is the total number of epidemiological weeks, i
is the current week in simulation, Ȳi is the number of newly
reported cases in real life and Yi is the number of new cases
n
in simulation).
1X
M SE =
(Ȳi − Yi )2
(3)
n i=1
Sr parameter was found to be significantly sensitive, and
gave best results when tuned to 3 meters. The second parameter for sensitivity analysis was Mm , a mosquito’s maximum number of meals in a day. It was varied for three
different values and errors were recorded (Figure 6). Mm
was then fixed to 1 to minimize the error. Pm , Pf and Mr
were likewise fixed to 0.2, 0.5 and 0.05 respectively as they
on average gave approximately constant mosquito population.
3.2 Training
Model parameters were tuned using trial and error to give
a good fit on training data. The results were animated as
a simulation and were graphically represented. Error was
derived with respect to the historical/training data. Sensitivity analysis was conducted to determine the effect of
each parameter on the model’s output and the more sensitive parameters were made sufficiently accurate to reduce
the error [25].
A slight error margin was left while training because training data only consists of reported cases, while due to its non
fatal nature, some number of chikungunya infections go unreported [1, 3].
The entire population of even a small city cannot be taken
into consideration due to computational in-feasibility. The
model simulation was accomplished considering 1000 human
individuals and 2000 mosquitoes involved in a chikungunya
epidemic and interacting at a city scale, in case of training
location.
Considering that the population density of the testing location is only about half that of the training location, and
Figure 6: Mm : Mean-Squared Error recorded for different
Mm values
Figure 7 shows how the ABM was fit into the historical
data. An error of ±9 cases was left to account for unreported
cases.
431
Table 1: ABM Parameters
Parameter
Mosquito Parameters:
Fs
Fr
As ,Ae
Mm
Mr
Pm
Oc
Pf
Sr
Infection Transmission Cycle Parameters:
α
β
Infection Cycle Parameters:
nb infected init
Ne
Ni
Prc
Pirc
Human Parameters:
Pp1
Pp2
Description
Value
Reference
Flying speed
Maximum distance
Active period
Maximum number of meals in a day
Mortality rate
Probability of an adult female to mate successfully
Ovipositioning behavior (single (0) or spread over multiple sites (1))
Probability that the hatching egg will be female
Sensory range
0.0...1.0 km/hr
350m
7:00 a.m., 6:00 p.m.
1
0.05/day*
0.2
1
0.5
3m
[5]
[45]
[8]
Trained
[45]
Trained
[8]
Trained
Trained
Transmission probability of infection from mosquito to human
Transmission probability of infection from human to mosquito
0.6
0.275
[17]
[17]
Initial number of infected people
Number of days a human spends in exposed state
Number of days a human spend in infected state
Probability of transiting from recovered state to susceptible state
Probability that passing infection leaves human in chronic state
2
2...6 days
4...7 days
0
0.95
[47]
[9]
[9]
[48]
[9]
Probability of a Type 1 agent of going to park at 4:00 p.m.
Probability of a Type 2 agent of going to park at 4:00 p.m.
0.5
0.1
Trained
Trained
* [45] proposes 0.2/day mortality rate which was reduced considering the relatively low mosquito/human ratio in the model.
Figure 7: St. Martin Epidemic (Training): Results
from training the model on the St. Martin epidemic
Figure 8: St. Barthélemy epidemic (Testing): Results
from testing the model on the St. Barthélemy epidemic
3.3 Testing
real epidemic and used it for analyses of different prevention
strategies on the test location.
Figure 8 shows the results when the trained model was
ran to check the effects of a chikungunya epidemic in Saint
Barthélemy and results were compared with the actual 2014
chikungunya epidemic of the same. The error encountered
was ± 0.54 cases, nearly insignificant, indicating that our
model scales well to changing population size. The initial
results are a little less than the reported results which may
very well be from the fact that by the time the first case
was recorded, the infection had already spread through the
environment in the real world, while the model is initialized
as infection-free. It also suggest estimates on certain Ae.
aegypti parameters like sensory range (3 meters) and average
feeding frequency (1 meal/day).
The results obtained show that ABMs can provide very
accurate results when used to model the complex epidemiology of mosquito-borne diseases. They also provide estimates
on certain mosquito parameters like sensory range, feeding
frequency, etc. which are difficult to measure otherwise.
4.
4.1 Strategies
No vaccine exists to prevent chikungunya virus infection.
It can only be prevented by avoiding mosquito bites either
at the individual level or by reducing the mosquito population [12]. Keeping this in mind, two popular paradigms of
mosquito prevention were implemented, analyzed and compared using the above model:
1. Centralized Prevention Strategies: In this case, there
is a centralized organization dedicated to reducing the
mosquito population through methods like detection
and elimination of breeding places, proper covering of
persistent water sources, and reliable water supply [37].
We choose LSM (Larval Source Management), which
is economical and very popular, as a strategy. Its per
sq km associated annual cost when adjusted for 2016
prices [11], comes to US$6000 [26].
PREVENTION STRATEGIES
2. Decentralized Prevention Strategies: Here people adopt
prophylactic measures like use of mosquito repellent
creams, liquids, coils, mats, etc., or full body coverings
As the model performed well in the validation phase, we
assumed that it is a reasonably effective representation of the
432
to prevent mosquito bites. One person can be protected for an year at a cost of US$10 with insecticidetreated nets (ITNs); indoor residual spraying (IRS)
costs US$180/building [22, 24].
All costs mentioned above are as quoted by private agencies. They may be brought down significantly by conducting
large-scale mosquito- control programs, and with relevant
government subsidies.
For comparison of the two strategies, the two iterations
were initialized with same resources, i.e., the same initial
budget of US$ 20,000. Considering it would cost approximately US$ 30,000/year to cover a town of 5 sq km completely for a larvicide program, we assume that only 66% of
the larval habitats are found and treated. This is consistent
with the fact that larval habitats may be small and widely
dispersed, making it difficult to locate all of them [14]. For
the second strategy (ITN+IRS), resources worth 20,000 US$
were distributed randomly among the population (220 US$
per household) helping individuals in the population avoid
mosquito bites in their households.
Figure 10: Mosquito Population (Strategy 1): Number
of Mosquitoes and Eggs per Day
4.2 Outcomes
Strategy 1 (LSM) was found to be more effective at completely eliminating the infection from both the human and
mosquito populations within 5 weeks. Strategy 2 took 7
weeks to do the same. Not trying to contain the infection
kept it going even after 13 weeks (Figure 9). This difference in effectiveness may be from the fact that Strategy 2 is
mostly useful during the night time when most individuals
are back to their households, while A. Aegypti is a day-biting
mosquito.
Figure 11: Mosquito Population (Strategy 2): Number
of Mosquitoes and Eggs per Day
quantitative analyses of mosquito-borne epidemics. This
and other such models carry high practical value as they can
be used to quickly try out different combinations of strategies, study the effects of infection on different population
groups, find high risk groups, plan vaccination programs,
and categorize locations with respect to their seasonal risk
factor. They can also be used to arrive at estimates of vector parameters (such as the mosquito’s sensing range) that
are not easy to measure directly. The case study demonstrated how the model was accurately able to trace the evolution of the infection, given data from a past epidemic in
a similar location is provided. It also predicted that on a
low budget, centralized strategies like larval source management are more effective compared to individual measures
like insecticide-treated bed nets and indoor residual spraying. Though the above model has been tested on tropical
climate of Caribbean Islands, it can be easily extended to
other locations provided relevant training data are available.
The model can also be extended to consider mutations
of infection [18], actual human mobility patterns, multiple
mosquito species, and other factors like wind velocity.
Figure 9: Prevention Strategies: Results from testing the
two strategies
Strategy 1 also had a much greater effect on mosquito population, reducing it by 70% while Strategy 2 only reduced it
by 25% (Figure 10 and Figure 11). The results of both the
strategies were found to be consistent with past studies [31,
40].
From the fact that in most cases a mosquito’s life cycle
is not greatly dependent on the presence or absence of the
infection due to their short lifespan [19], it can be reasoned
that the above results will hold true for other diseases spread
by A. Aegypti, like the presently prominent Zika virus.
5.
Acknowledgements
The authors would like to thank Barbara Han for giving
insights on mosquito behavior.
REFERENCES
CONCLUSION AND DISCUSSION
Diseases like chikungunya and dengue which currently have
no vaccine, need proactive measures to prevent or contain
their breakout. Our ABM provides a good mechanism for
[1] Chikungunya fever guide.
http://www.chikungunya.in/, 2016. Accessed:
2016-05-06.
433
[2] Importation of gis data. https://github.com/
gama-platform/gama/wiki/LuneraysFlu_step3, 2016.
Accessed: 2016-5-15.
[3] D. Almond. What is the state of the Caribbean
chikungunya epidemic now?, 2015. Accessed:
2016-05-06.
[4] S. M. N. Arifin, G. J. Davis, and Y. Zhou. A spatial
agent-based model of malaria: Model verification and
effects of spatial heterogeneity. Int. J. Agent Technol.
Syst., 3(3):17–34, July 2011.
[5] I. Bargielowski, C. Kaufmann, L. Alphey, P. Reiter,
and J. Koella. Flight performance and teneral energy
reserves of two genetically-modified and one wild-type
strain of the yellow fever mosquito Aedes aegypti.
Vector-Borne and Zoonotic Diseases,
12(12):1053–1058, July 2012.
[6] M. Barrientos and C. Soria. Saint Barthelemy age
structure. http://www.indexmundi.com/saint_
barthelemy/age_structure.html, 2015. Accessed:
2016-04-12.
[7] D. Bleijs. Aedes albopictus. http://www.
chikungunyavirusnet.com/aedes-albopictus.html,
2014. Accessed: 2016-04-12.
[8] D. Bleijs. Aedes aegypti. http:
//www.denguevirusnet.com/aedes-aegypti.html,
2016. Accessed: 2016-04-12.
[9] D. A. Bleijs. Chikungunya signs clinical symptoms.
http://www.chikungunyavirusnet.com/
signs-a-symptoms.html, 2016. Accessed: 2016-04-12.
[10] O. J. Brady, M. A. Johansson, C. A. Guerra, S. Bhatt,
N. Golding, D. M. Pigott, H. Delatte, M. G. Grech,
P. T. Leisnham, and R. e. a. Maciel-de Freitas.
Modelling adult Aedes aegypti and Aedes albopictus
survival at different temperatures in laboratory and
field settings. Parasites |& Vectors, 6(1), Dec. 2013.
[11] U. I. Calculator. Us inflation calculator.
http://www.usinflationcalculator.com/, 2016.
Accessed: 2016-5-15.
[12] CDC. Chikungunya virus.
http://www.cdc.gov/chikungunya/prevention/,
2016. Accessed: 2016-05-06.
[13] CDC. Dengue and the Aedes aegypti mosquito.
http://www.cdc.gov/dengue/resources/30Jan2012/
aegyptifactsheet.pdf, 2016. Accessed: 2016-05-06.
[14] CDC. Larval control and other vector control
interventions.
http://www.cdc.gov/malaria/malaria_worldwide/
reduction/vector_control.html, 2016. Accessed:
2016-05-06.
[15] R. Connell, P. Dawson, and A. Skvortsov. Comparison
of an agent-based model of disease propagation with
the generalised sir epidemic model. Technical report,
DTIC Document, 2009.
[16] C. Deng, H. Tao, and Z. Ye. Agent-based modeling to
simulate the dengue spread. In Proceedings of SPIE The International Society for Optical Engineering
7143, Nov. 2008.
[17] C. J. Dommar, R. Lowe, M. Robinson, and X. Rodó.
An agent-based model driven by tropical rainfall to
understand the spatio-temporal heterogeneity of a
chikungunya outbreak. Acta Tropica, 129:61–73, Jan.
2014.
[18] J. Z. Farkas, S. A. Gourley, R. Liu, and A.-A. Yakubu.
Using Mathematics at AIM to Outwit Mosquitoes.
Notices Amer. Math. Soc., 63(03):292–293, 2016.
[19] H. M. Ferguson and A. F. Read. Why is the effect of
malaria parasites on mosquito survival still
unresolved? Trends in parasitology, 18(6):256–261,
June 2002.
[20] S. Fischer, I. S. Alem, M. S. De Majo, R. E. Campos,
and N. Schweigmann. Cold season mortality and
hatching behavior of Aedes aegypti L. (Diptera:
Culicidae) eggs in Buenos Aires City, Argentina.
Journal of Vector Ecology, 36(1):94–99, 2011.
[21] S. Fu and G. Milne. Epidemic modelling using cellular
automata. In Proc. of the Australian Conference on
Artificial Life. Citeseer, 2003.
[22] GiveWell. Mass distribution of long-lasting
insecticide-treated nets (LLINs).
http://www.givewell.org/international/
technical/programs/insecticide-treated-nets,
2016.
[23] A. Grignard, P. Taillandier, B. Gaudou, D. A. Vo,
N. Q. Huynh, and A. Drogoul. GAMA 1.6: Advancing
the art of complex agent-based modeling and
simulation. Lecture Notes in Computer Science, pages
117–131, 2013.
[24] Hicare.in. Make your home safe today. expert
mosquito control service.
http://hicare.in/mosquito_control/, 2016.
Accessed: 2016-5-15.
[25] Y. Huang, X. Xiang, G. Madey, and S. E. Cabaniss.
Agent-based scientific simulation. Comput. Sci. Eng.,
7(1):22–29, 2005.
[26] ICMR. Urban mosquito control - a case study. ICMR
Bulletin, 30(3), 2000.
[27] C. Illangakoon, R. D. McLeod, and M. R. Friesen.
Agent based modeling of malaria. In Humanitarian
Technology Conference - (IHTC), 2014 IEEE Canada
International, June 2014.
[28] C. Isidoro, N. Fachada, F. Barata, and A. C. Rosa.
Artificial life model of dengue host-vector disease
propagation. In International Joint Conference on
Computational Intelligence, pages 243–247, Oct. 2009.
[29] N. Kamaladhasan, B. K. Tyagi, P. S. Swamy, and
S. Chandrasekaran. Studies on the maintenance of
’self-sustained’ mosquito vector population in Vaigai
river, South India. Current Science, 110(1):57–68,
2016.
[30] A. Kleczkowski and B. T. Grenfell. Mean-field-type
equations for spread of epidemics: The small world
model. Physica A: Statistical Mechanics and its
Applications, 274(1):355–360, 1999.
[31] E. Majambere, SilasWorrall. Potential and
costeffectiveness of lsm, 2007.
[32] F. Miksch, P. Pichler, K. J. P. Espinosa, K. S. T.
Casera, A. N. Navarro, and M. Bicher. An agent-based
epidemic model for dengue simulation in the
philippines. In 2015 Winter Simulation Conference
(WSC), pages 3202–3203, Dec 2015.
[33] S. M.Niaz Arifin, R. Reaz Arifin, D. De, A. Pitts, and
G. R. Madey. Integrating an agent-based model of
malaria mosquitoes with a geographic information
system. In The 25th European Modeling and
434
[43] N. H. Shah and J. Gupta. SEIR model and simulation
for vector borne diseases. Applied Mathematics,
4(08):13, 2013.
[44] S. Swarup, S. G. Eubank, and M. V. Marathe.
Computational epidemiology as a challenge domain for
multiagent systems. In Proceedings of the 2014
international conference on Autonomous agents and
multi-agent systems, pages 1173–1176. International
Foundation for Autonomous Agents and Multiagent
Systems, 2014.
[45] C. J. Thomas, D. E. Cross, and C. Bøgh. Landscape
movements of Anopheles gambiae malaria vector
mosquitoes in Rural Gambia. PloS one, 8(7):e68679,
July 2013.
[46] S. Thomas, U. Obermayr, D. Fischer, J. Kreyling, and
C. Beierkuhnlein. Low-temperature threshold for egg
survival of a post-diapause and non-diapause
European aedine strain, Aedes albopictus (Diptera:
Culicidae). Parasites |& Vectors, 5(1), May 2012.
[47] W. Van Bortel, F. Dorleans, J. Rosine, A. Blateau,
D. Rousset, S. Matheus, I. Leparc-Goffart, O. Flusin,
C. Prat, R. Cesaire, et al. Chikungunya outbreak in
the Caribbean region, December 2013 to March 2014,
and the significance for Europe. Eurosurveillance,
19(13), Apr. 2014.
[48] WHO. Chikungunya.
http://www.who.int/denguecontrol/arbo-viral/
other_arboviral_chikungunya/en/, 2016. Accessed:
2016-04-12.
[49] WHO. Vector borne diseases. http:
//www.who.int/mediacentre/factsheets/fs387/en/,
2016. Accessed: 2016-04-12.
[50] V. Wiwanitkit. Vaccination against mosquito borne
viral infections: current status. Iran J Immunol,
4(4):186–196, 2007.
Simulation Symposium (EMSS 2013), Sept. 2013.
[34] S. M. Mniszewski, C. A. Manore, C. Bryan, S. Y.
Del Valle, and D. Roberts. Towards a hybrid
agent-based model for mosquito borne disease. In
Proceedings of the 2014 Summer Simulation
Multiconference (SummerSim ’14), pages 10:1–10:8,
2014.
[35] A. Mohammed and D. D. Chadee. Effects of different
temperature regimens on the development of Aedes
aegypti (L.) (Diptera: Culicidae) mosquitoes. Acta
Tropica, 119(1):38–43, Apr. 2011.
[36] L. Mowatt and S. T. Jackson. Chikungunya in the
Caribbean: An epidemic in the making. Infect Dis
Ther, 3(2):63–68, 2014.
[37] M. of Health and G. o. I. Welfare. Vector control
measures.
http://www.nvbdcp.gov.in/dengue12.html, 2016.
Accessed: 2016-05-06.
[38] L. Osborn. Caribbean weather in December.
http://bit.ly/1Tn8zAj, 2016. Accessed: 2016-04-12.
[39] PAHO. Chikungunya: Statistic data.
http://bit.ly/1KA6cUE, 2016. Accessed: 2016-05-06.
[40] S. Pang, L. Chiang, C. Tan, I. Vythilingam,
S. Lam-Phua, and L. Ng. Low efficacy of
delthamethrin-treated net against singapore aedes
aegypti is associated with kdr-type resistance. Tropical
Biomedicine, 32(1):140–50, Mar. 2015.
[41] L. Perez and S. Dragicevic. An agent-based approach
for modeling dynamics of contagious disease spread.
International journal of health geographics, 8(1):1,
2009.
[42] S. F. Railsback, S. L. Lytinen, and S. K. Jackson.
Agent-based simulation platforms: Review and
development recommendations. Simulation,
82(9):609–623, Mar. 2006.
435